High entropy mxenes and methods of making thereof

ABSTRACT

A Composition of matter defined by the general formula of M1M2M3M4X 3  wherein: X is carbon; and M1, M2, M3, and M4 each represent a different transition metal selected from the group consisting of Ti, Ta, Sc, Cr, Zr, Hf, Mo, V, and Nb.

RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationSer. 63/089,811, filed on Oct. 9, 2020, the entire disclosure of whichbeing hereby expressly incorporated herein by reference.

GOVERNMENT RIGHTS

None.

TECHNICAL FIELD

Aspects of this disclosure relate to rechargeable battery technologies.More specifically, embodiments relate to carbide materials capable ofaccommodating ions and molecules during intercalation.

BACKGROUND

Battery technologies have been considered as the key to realization oflong range electric vehicles and efficient large scale grid storageapplications. Despite the great progress in research on advanced batterytechnologies, challenges still exist to increase the energy and powderdensities, reduce the cost, and improve the safety and life of thebatteries. Of the new electrode materials, two-dimensional (2D) solidsare of particular interest due to their large areas ofelectrochemically-active surfaces. Having a new family of 2D structureswith a wide range of chemistries can provide a source of materials forvarious applications.

SUMMARY

According to one embodiment, the present disclosure provides acomposition of matter defined by the general formula of M1M2M3M4X₃,wherein: X is carbon; and M1, M2, M3, and M4 each represent a differenttransition metal selected from the group consisting of Ti, Ta, Sc, Cr,Zr, Hf, Mo, V, and Nb. In one aspect of this embodiment, M1, M2, M3, M4each represent a different transition metal selected from the groupconsisting of Ti, Ta, Cr, Mo, V, and Nb. In yet another aspect of thisembodiment, the composition is selected from the group consisting ofTiVNbMoC₃ and TiVCrMoC₃. In another aspect of this embodiment, thecomposition is a MXene. In yet another aspect of this embodiment, thecomposition is produced by at least: preparing precursor MAX phasepowder; etching the MAX phase powder to obtain multi-layered MXenepowder; and delaminating the multi-layered MXene powder to obtainsingle-to-few-layered MXene flakes. In another aspect of thisembodiment, preparing precursor MAX phase powder includes mixing andreactive sintering elemental powders of equimolar ratio of fourtransition metals M¹, M², M³, and M⁴ with Al and C M¹:M²:M³:M⁴:Al:C in1:1:1:1:1.1:2.7 stoichiometric ratio to obtain one or more sintered MAXphase blocks. In yet another aspect of this embodiment, preparingprecursor MAX phase powder further includes milling the one or moresintered MAX phase blocks to obtain the MAX phase powder. In a variantaspect of this embodiment, etching the MAX phase powder includes addingthe MAX phase powder into an aqueous hydrofluoric acid to selectivelyetch away Al to obtain multi-layered MXene powder. In a variant aspectof this embodiment, delaminating the multi-layered MXene powder includesdelaminating the multi-layered MXene powder using tetramethylammoniumhydroxide (TMAOH). In yet another aspect of this embodiment,delaminating the multi-layered MXene powder further includes filteringMXene from TMAOH to obtain the single-to-few-layered MXene flakes.

According to one embodiment, the present disclosure provides a method ofproducing a composition of matter defined by the general formula ofM1M2M3M4X3, the method includes: preparing precursor MAX phase powder;etching the MAX phase powder to obtain multi-layered MXene powder; anddelaminating the multi-layered MXene powder to obtainsingle-to-few-layered MXene flakes having the general formula ofM1M2M3M4X3, wherein: X is carbon; and M1, M2, M3, and M4 each representa different transition metal selected from the group consisting of Ti,Ta, Sc, Cr, Zr, Hf, Mo, V, and Nb. In one aspect of this embodiment, M1,M2, M3, M4 each represent a different transition metal selected from thegroup consisting of Ti, Ta, Cr, Mo, V, and Nb. In yet another aspect ofthis embodiment, the composition is selected from the group consistingof TiVNbMoC₃ and TiVCrMoC₃. In another aspect of this embodiment, thecomposition is a MXene. In yet another aspect of this embodiment, thecomposition is produced by at least: preparing precursor MAX phasepowder; etching the MAX phase powder to obtain multi-layered MXenepowder; and delaminating the multi-layered MXene powder to obtainsingle-to-few-layered MXene flakes. In another aspect of thisembodiment, preparing precursor MAX phase powder includes mixing andreactive sintering elemental powders of equimolar ratio of fourtransition metals M¹, M², M³, and M⁴ with Al and C M¹:M²:M³:M⁴:Al:C in1:1:1:1:1.1:2.7 stoichiometric ratio to obtain one or more sintered MAXphase blocks. In yet another aspect of this embodiment, preparingprecursor MAX phase powder further includes milling the one or moresintered MAX phase blocks to obtain the MAX phase powder. In a variantaspect of this embodiment, etching the MAX phase powder includes addingthe MAX phase powder into an aqueous hydrofluoric acid to selectivelyetch away Al to obtain multi-layered MXene powder. In a variant aspectof this embodiment, delaminating the multi-layered MXene powder includesdelaminating the multi-layered MXene powder using tetramethylammoniumhydroxide (TMAOH). In yet another aspect of this embodiment,delaminating the multi-layered MXene powder further includes filteringMXene from TMAOH to obtain the single-to-few-layered MXene flakes.

According to one embodiment, the present disclosure provides acomposition of matter defined by the general formula of M1M2M3M4AX3,wherein: X is carbon; A is Al, and M1, M2, M3, and M4 each represent adifferent transition metal selected from the group consisting of Al, Ti,Ta, Sc, Cr, Zr, Hf, Mo, V, and Nb.

While multiple embodiments are disclosed, still other embodiments of thepresent disclosure will become apparent to those skilled in the art fromthe following detailed description, which shows and describesillustrative embodiments of the disclosure. Accordingly, the drawingsand detailed description are to be regarded as illustrative in natureand not restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

The figures described herein are for illustration purposes only. Thefigures are not intended to limit the scope of the present disclosure.

FIG. 1A is a simplified schematic showing reactive sintering ofhigh-entropy MAX phases, in accordance with embodiments of thedisclosure.

FIG. 1B is a simplified schematic showing a high-entropy MAX unit cell,in accordance with embodiments of the disclosure.

FIG. 1C is a simplified schematic showing multi-layer high-entropyMXenes, in accordance with embodiments of the disclosure.

FIG. 1D is a simplified schematic showing single flakes of high-entropyMXenes, in accordance with embodiments of the disclosure.

FIG. 2A shows XRD patterns of high-entropy TiVNbMoAlC₃ MAX andTiVNbMoC₃T_(x) MXenes, in accordance with embodiments of the disclosure.

FIG. 2B shows XRD patterns of high-entropy TiVCrMoAlC₃ MAX andTiVCrMoC₃T_(x) MXenes, in accordance with embodiments of the disclosure

FIG. 3A is a SEM image of MAX powder of TiVNbMoAlC₃, in accordance withembodiments of the disclosure.

FIG. 3B is a SEM image of MAX powder of TiVCrMoAlC₃, in accordance withembodiments of the disclosure.

FIG. 3C is a SEM image of etched multi-layer MXene powder ofTiVNbMoC₃T_(x), in accordance with embodiments of the disclosure.

FIG. 3D is a SEM image of etched multi-layer MXene powder ofTiVCrMoC₃T_(x), in accordance with embodiments of the disclosure.

FIG. 3E is a SEM image of a single film of TiVNbMoC₃T_(x) MXene flake,in accordance with embodiments of the disclosure.

FIG. 3F is a SEM image of a filtered film of TiVCrMoC₃T_(x) MXene, inaccordance with embodiments of the disclosure.

FIG. 4A-4F are XPS spectra of TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x), inaccordance with embodiments of the disclosure.

FIG. 4G shows atomic % vs Ar+ etching time for TiVNbMoC₃T_(x), inaccordance with embodiments of the disclosure.

FIG. 4H shows atomic % vs Ar+ etching time for TiVCrMoC₃T_(x), inaccordance with embodiments of the disclosure.

FIG. 4I shows a High-angle annular dark-field (HAADF) STEM images ofTiVNbMoC₃T_(x) MXene, in accordance with embodiments of the disclosure.

FIG. 4J shows HAADF STEM images combined with EDS results ofTiVNbMoC₃T_(x) (top) and TiVCrMoC₃T_(x) (bottom), in accordance withembodiments of the disclosure.

FIG. 5A shows differential scanning calorimetry results ofTi:V:Nb:Mo:1.1Al:2.7C powder mixture under argon flow, in accordancewith embodiments of the disclosure.

FIG. 5B shows differential scanning calorimetry results ofTi:V:Cr:Mo:1.1Al:2.7C powder mixture under argon flow, in accordancewith embodiments of the disclosure.

FIG. 6 shows four representative SEM images of TiVNbMoAlC₃ MAX particlesthat were used for EDS, in accordance with embodiments of thedisclosure.

FIG. 7 shows four representative SEM images of TiVCrMoAlC₃ MAX particlesthat were used for EDS, in accordance with embodiments of thedisclosure.

FIG. 8A shows XRD patterns of multiphases formed by sintering differentratios of Ti:V:Nb:Mo with Mo variation, in accordance with embodimentsof the disclosure.

FIG. 8B shows XRD patterns of multiphases formed by sintering differentratios of Ti:V:Nb:Mo with Nb variation, in accordance with embodimentsof the disclosure.

FIG. 8C shows XRD patterns of multiphases formed by sintering differentratios of Ti:V:Cr:Mo with Cr variation, in accordance with embodimentsof the disclosure.

FIG. 9A shows a single-flake TiVCrMoC₃T_(x) MXene solution afterdelamination with TMAOH, in accordance with embodiments of thedisclosure.

FIGS. 9B-9C show few-layer TiVCrMoC₃T_(x) MXene clay post delamination,in accordance with embodiments of the disclosure.

FIG. 9D shows TiVCrMoC₃T_(x) MXene film doctor-bladed on a filter paper,in accordance with embodiments of the disclosure.

FIG. 9E shows a single-flake TiVCrMoC₃T_(x) MXene solution afterdelamination with TMAOH, in accordance with embodiments of thedisclosure.

FIGS. 9F-9G show few-layer TiVNbMoC₃T_(x) MXene clay post delamination,in accordance with embodiments of the disclosure.

FIG. 9H shows TiVNbMoC₃T_(x) MXene film doctor-bladed on a filter paper,in accordance with embodiments of the disclosure.

FIG. 10A is a SEM image showing a cross-sectional view of TiVNbMoC₃T_(x)few-layered films, in accordance with embodiments of the disclosure.

FIG. 10B is a SEM image showing a cross-sectional view of TiVCrMoC₃T_(x)few-layered films, in accordance with embodiments of the disclosure.

FIG. 10C is a SEM image showing a top view of TiVNbMoC₃T_(x) few-layeredfilms, in accordance with embodiments of the disclosure.

FIG. 10D is a SEM image showing a top view of TiVCrMoC₃T_(x) few-layeredfilms, in accordance with embodiments of the disclosure.

FIG. 11 shows XPS spectra of TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x), inaccordance with embodiments of the disclosure.

FIG. 12 shows high-angle annular dark-field (HAADF) STEM images ofdelaminated TiVNbMoC₃T_(x) (left) and TiVCrMoC₃T_(x) (right) MXenes,HAADF STEM image of TiVCrMoC₃T_(x) with EDS data indicating atomicdistribution of Ti, V, Cr, Mo, C atoms, in accordance with embodimentsof the disclosure.

FIG. 13 shows calculated electron concentration of synthesized MAXphases with reference to their relative formation energy, in accordancewith embodiments of the disclosure.

FIG. 14 shows calculated configurational entropy in a two, three, andfour-component solid solutions as a function of mol % of the N_(th)component.

DETAILED DESCRIPTION

While the disclosed subject matter is amenable to various modificationsand alternative forms, specific embodiments have been shown by way ofexample in the drawings and are described in detail below. Theintention, however, is not to limit the subject matter disclosed hereinto the particular embodiments described. On the contrary, the disclosureis intended to cover all modifications, equivalents, and alternativesfalling within the scope of the subject matter disclosed herein, and asdefined by the appended claims.

Aspects of the present disclosure relate to MXenes. MXenes may refer to2D transition metal carbines and nitrides having n+1 (e.g., n=1 to 4)atomic layers of transition metals interleaved by carbon and/or nitrogenlayers. MXenes may be described as having a chemical formula ofM_(n+1)X_(n)T_(x) (n=1 to 4), where a 2D MXene flake may be comprised ofn+1 atomic layers of transition metals (M) from groups 3 to 6 of theperiodic table interleaved by a layer of carbon and/or nitrogen (X)between the M layers. For example, transition metal may be Sc, Ti, V,Cr, Y, Zr, Nb, Mo, Hf, or Ta. In addition, the outer transition metalatomic layers may be bonded to surface terminations (T), such as —O, —F,and —OH. MXenes may exhibit superior metallic electrical conductivity,high in-plane mechanical stiffness, and impressive catalytic as well aselectrochemically active behavior. MXenes may be synthesized from theirprecursors, the MAX phases, by selective etching of the A layers whichmay be from group 13-16 of the periodic table, such as Al.

Aspects of the present disclosure relate to synthesis of high-entropyMXenes and synthesis of MXene precursors of layered multi-principalelement (MPE) MAX carbides. Specifically, aspects of the presentdisclosure relate to high-entropy (e.g., more than 3 principal elements)two-dimensional (2D) carbide MXenes, including carbide MXenes includingfour or more transition metals such as TiVNbMoC₃ and TiVCrMoC₃.Additionally, aspects of the present disclosure relate to precursorhigh-entropy MAX phases of the high-entropy two-dimensional (2D) carbideMXenes such as TiVNbMoAlC₃ and TiVCrMoAlC₃. Aspects of the presentdisclosure relate to pure single-phase high-entropy MXenes.

A method of synthesizing MPE MXene according to the present disclosureincludes synthesizing single-phase purity layered MPE MAX carbides(e.g., TiVNbMoAlC₃ and TiVCrMoAlC₃), and exfoliating and delaminatingthe single-phase purity layered MPE MAX carbides to obtain MPE MXenes(e.g., TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x)). In the synthesizedhigh-entropy phases, the transition metal stoichiometric ratios may beretained at 1:1:1:1 (±0.2) for M¹:M²:M³:M⁴.

FIGS. 1A-1D depicts a method of synthesizing TiVNbMoC₃T_(x) andTiVCrMoC₃T_(x) MXenes according to the present disclosure. In variousembodiments, high-entropy MAX phases TiVNbMoAlC₃ and TiVCrMoAlC₃ (FIG.1B) may be synthesized by reactive sintering of elemental powders (FIG.1A), which includes mixing an equimolar ratio of four transition metalsM¹, M², M³, and M⁴ with Al and C M¹:M²:M³:M⁴:Al:C in 1:1:1:1:1.1:2.7stoichiometric ratio, reactive sintering the powders to obtain sinteredblocks of the high-entropy MAX phases, and milling the sintered blocksof high-entropy MAX phases to obtain fine powders of the high-entropyMAX phases. As depicted, reactive sintering may be performed in a tubefurnace with the powder mixtures placed in alumina crucibles and byheating the powder mixtures from room temperature to 1600° C. at 3°C./min in a tube furnace and holding time of 4 hours under argonatmosphere.

FIGS. 5A-5B show differential scanning calorimetry results ofTi:V:Nb:Mo:1.1Al:2.7C and Ti:V:Cr:Mo:1.1Al:2.7C powder mixtures underargon flow. Both powder mixtures have a peak between 653-664° C., whichindicates the melting of Al and the start of reaction with thetransition metals to form intermetallics. Binary can form with theinitiation of carbon diffusion, followed by phase stabilization andternary carbon formation between 1250-1350° C. At temperatures above1450° C., high-entropy multi-principal element phases may form. Thehigh-entropy MAX phases TiVNbMoAlC₃ and TiVCrMoAlC₃, as synthesized,include layered transition metal layers comprised of four transitionmetal elements (i.e., Ti, V, Nb or Cr, and Mo) with aluminum and carbonatomic layers in a M₄AlC₃ MAX structure.

X-ray diffraction (XRD) may be used to analyze the sintered powders toverify the formation of high-entropy MAX phases. Specifically, thebottom patterns in FIGS. 2A-2B show the XRD spectra of sintered powdersTi:V:Nb:Mo:Al:C and Ti:V:Cr:Mo:Al:C, verifying the formation ofTiVNbMoAlC₃ and TiVCrMoAlC₃ MAX phases. As shown, the spectra confirmsthe presence of M₄AlC₃ MAX phase peaks and their a-lattice parameters(a-LPs) were determined, based at least in part upon the characteristic(001) and in-plane peaks, to be 3.038 and 2.97 Å and c-LPs of 23.590 and22.978 Å for TiVNbMoAlC₃ and TiVCrMoAlC₃, respectively. Additionalcharacterization may be performed to identify the presence, if any, ofimpurity phases in the sintered powders. Common impurities may includevery small amounts of Al—Mo and Mo—V intermetallics in both TiVNbMoAlC₃and TiVCrMoAlC₃. As shown, the XRD spectra do show a very small numberof intermetallic impurities but with no other clearly identifiablecarbide or oxide impurities. The equimolar high-entropy stabilizationsynthesis method used by the present disclosure is thus verified as aneffective method for forming highly pure M₄AlC₃ MAX phases, precursorsto high-entropy MXenes.

In addition to XRD analysis, energy-dispersive x-ray spectroscopy (EDS)combined with scanning electron microscopy (SEM) may be used tocharacterize the resultant composition of the formed MAX phases. Todistinguish the compositions in the resulting MAX phases, EDS pointscans on several MAX particles shown in SEM micrographs may be performed(FIGS. 3A-3B). As an example, the average EDS results for the fourtransition metals in each composition are shown in Table 1 forTiVNbMoAlC₃ and TiVCrMoAlC₃. Representative SEM images of the MAXparticles that were used for EDS are shown for TiVNbMoAlC₃ andTiVCrMoAlC₃ in FIGS. 6-7. These results indicate an equimolar ratio ofthe four transition metals as Ti:V:Nb:Mo0.9±0.2:10.1±0.2:10.1±0.2:0.9±0.3 and Ti:V:Cr:Mo ratio of10.0±0.1:10.1±0.1:10.0±0.1:0.9±0.1. Al content was observed to be nearstoichiometric ratio of 1.1±0.2 in both MAX phases. The EDS resultsconfirm that the sintered powders are MPE MAX phases, specifically,TiVNbMoAlC₃ and TiVCrMoAlC₃.

TABLE 1 EDS on particles Ti V Cr Nb Mo Al (Ti, V, Nb, Mo)₄AlC₃ 0.9 ± 0.21.1 ± 0.2 — 1.1 ± 0.2 0.9 ± 0.3 1.09 ± 0.2  ML-(Ti, V, Nb, Mo)₄C₃T_(x)1.0 ± 0.1 1.0 ± 0.1 — 1.2 ± 0.4 0.8 ± 0.3 — d-(Ti, V, Nb, Mo)₄C₃T_(x)0.9 ± 0.2 1.0 ± 0.2 — 1.0 ± 0.2 0.9 ± 0.3 — (Ti, V, Cr, Mo)₄AlC₃ 1.0 ±0.1 1.1 ± 0.1 1.0 ± 0.1 — 0.9 ± 0.1 1.16 ± 0.15 ML-(Ti, V, Cr,Mo)₄C₃T_(x) 1.1 ± 0.2 1.2 ± 0.1 0.8 ± 0.3 — 0.9 ± 0.1 d-(Ti, V, Cr,Mo)₄C₃T_(x) 1.1 ± 0.2 1.1 ± 0.2 0.9 ± 0.2 — 1.0 ± 0.2 —

At least supported by the XRD and EDS characterizations, the method forsynthesizing MPE MAX phases according to the present disclosure isproven to achieve the effect of entropy stabilization to allow the useof four transition metals such as Ti—V—Nb—Mo or Ti—V—Cr—Mo combinationsto synthesize stable, homogeneous, and single-phase M₄AC₃ MAXstructures. The MPE MAX phases may be stabilized because ofconfigurational entropy, which may be absent in non-high-entropy MAXstructures.

The effect of entropy stabilization in TiVNbMoAlC₃ and TiVCrMoAlC₃ maybe verified by preparing non-equimolar mixtures of the transition metalswith lowered Mo and Nb content in (Ti,V,Nb,Mo)₄AlC₃ and lowered Crcontent in three mixtures in (Ti,V,Cr,Mo)₄AlC₃ from one to 0.7, 0.4, and0.1. The mixtures with lowered Mo content may have ratios of Ti:V:Nb:Mo1.1:1.1:1.1:0.7, 1.2:1.2:1.2:0.4, and 1.3:1.3:1.3:0.1 with Al:C 1.1:2.7.The non-equimolar mixtures may then be sintered at identical conditionsto those for the equimolar ratio TiVNbMoAlC₃ MAX phase. As indicated bythe XRD spectra (FIG. 8A), the resulting compositions were a mix ofM₄AlC₃ and M₂AlC MAX phases for all three non-equimolar mixtures withlowered Mo content. The mixtures with lowered Nb content may have ratiosof Ti:V:Nb:Mo 1.1:1.1:0.7:1.1, 1.2:1.2:0.4:1.2, and 1.3:1.3:0.1:1.3 withsimilar Al:C ratio of 1.1:2.7. As indicated by the XRD spectra (FIG.8B), the resulting compositions were non-pure M₄AC₃ phases with M₂ACimpurities for all three non-equimolar mixtures with lowered Nb content.The mixtures with lowered Cr content may have ratios of Ti:V:Cr:Mo1.1:1.1:0.7:1.1, 1.2:1.2:0.4:1.2, and 1.3:1.3:0.1:1.3 with Al:C 1.1:2.7.As indicated by the XRD spectra (FIG. 8C), the resulting compositionsinclude impurity phases. Although all the nine powder mixtures wereprepared and sintered at identical conditions to the equimolar ratiophases, XRD results indicated undesired M₂AlC MAX phases for all threenon-equimolar mixtures with lowered Cr content. The undesiredmultiphases in the non-equimolar mixtures may include a mixture of solidsolution phases. Simultaneous formation of two different MAX phasesinstead of a single-phase MPE in both TiVNbMoAlC₃ and TiVCrMoAlC₃ maysuggest that entropy controls the transition from multiphase to ahigh-entropy single-phase, similar to other high-entropy alloys andceramics.

Returning to the method of synthesizing TiVNbMoC₃T_(x) andTiVCrMoC₃T_(x) MXenes, etching of MAX phases may be performed using anaqueous hydrofluoric acid (HF) etching process. First, the sinteredpowders of TiVNbMoAlC₃ and TiVCrMoAlC₃ MAX phases may be added into 48%HF for four days at 55° C. to selectively etch Al atomic layers from thehigh-entropy MAX phases (FIG. 1C) followed by repeated washing to aneutral pH. The reaction pathways of high-entropy MAX phases in aqueousHF to high-entropy MXene formations are as follows:

TiVNbMoAlC₃ to TiVNbMoC₃

TiVNbMoAlC₃+3HF=TiVNbMoC₃+AlF₃+3/2H₂

TiVNbMoC₃+2H₂O=TiVNbMoC₃(OH)₂+H₂

TiVNbMoC₃+2HF=TiVNbMoC₃F2+H₂

TiVCrMoAlC₃ to TiVCrMoC₃

TiVCrMoAlC₃+3HF=TiVCrMoC₃+AlF₃+3/2H₂

TiVCrMoAlC₃+2H₂O=TiVCrMoC₃(OH)₂+H₂

TiVCrMoAlC₃+2HF=TiVCrMoC₃F₂+H₂

XRD spectra of the etched and dried powders (FIGS. 2A-2B, middlepatterns) show a shift of the (002) peak in both phases to 5.65° and5.84° for multilayer TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x), respectively,which indicates an increase in the inter-flake spacing of 3.85 Å and3.64 Å respectively, compared to their MAX phase precursors. The SEMimages of the as-etched powders of TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x)(FIGS. 3C-3D) show the accordion-like morphologies of multilayerpowders, as expected after high-concentration HF etching. The inserts onFIGS. 2A-2B shows the shifting of the (002) peak during the evolutionfrom MAX phase to multi-layer MXene and to single layer Maxene film.

After etching, the method of synthesizing TiVNbMoC₃T_(x) andTiVCrMoC₃T_(x) MXenes further includes delaminating the exfoliatedhigh-entropy MXenes into single flakes of 2D MXenes, such as usingtetramethylammonium hydroxide (TMAOH) (FIG. 1D). FIG. 9A shows blackcolloidal solutions resulted from delamination of TiVNbMoC₃T_(x) andTiVCrMoC₃T_(x) multilayer powders with TMAOH. These solutions containsingle-flake high-entropy MXenes (FIG. 3E, shown in an aluminasubstrate). The black colloidal solutions may next be filtered viavacuum-assisted filtration to obtain high-entropy MXene films (FIG. 3F,FIGS. 10A-10D). XRD spectra of the filtered films of TiVNbMoC₃T_(x) andTiVCrMoC₃T_(x) (FIGS. 2A-2B, top patterns) show only the basal planepeaks (001 peaks), which indicates MXene flake restacking duringfiltration. The most intense (002) peak positions are at 4.51° and 5.22°for TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x) films, respectively, which show anincreased inter-flake distance of 7.81 Å and 5.44 Å as compared to theoriginal MAX c-LPs spacing. In addition, the (002) peak ofTiVCrMoC₃T_(x) illustrates “double” (002) peaks, where the most intensepeak is at 5.22° with a less-intense shoulder peak at 5.65°. Thesedouble peaks indicate the partial drying of water molecules from theMXene film. TiVCrMoC₃T_(x) has low-intensity peaks between 31° to 40° 2θwhich do not correspond to (001) peaks. These peaks indicate non-basalplane reflections of MXene, which can be due to the remaining multilayerflakes of MXene particles as seen using cross-sectional SEM methods onthe TiVCrMoC₃T_(x) MXene film (FIG. 3F). The absence of non-basal planereflections in the TiVNbMoC₃T_(x) film and the relative low intensity ofnon-basal plane peaks in comparison to the highly intense (002) peaks inTiVCrMoC₃T_(x) indicate that both films are either entirely or mostly,respectively, comprised of highly ordered single-to-few layers ofhigh-entropy MXene flakes.

EDS and SEM may be performed to verify the composition of the etchedmulti-layer high-entropy MXene powders (FIGS. 3C-3D). The EDS pointscans on the multilayer particles of TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x)are presented in Table 1, which indicate that the MXene multilayersheets retain their transition metals stoichiometric ratios of the MAXphase precursors (FIGS. 3A-3B) after HF etching. EDS results also showthat Mo and Cr molar ratios in the measured multilayer particles areslightly lower than those in their respective MAX precursors (Table 1).The slightly lower concentration of Cr in the multi-layer high-entropyMXenes may be attributed to relatively weaker Cr—C bonds compare toother M-C bonds and the more reactive nature of Cr-containing MXenesduring selective etching. In addition to entropy stabilization, thetendency of Mo and Cr to prefer the outer transition metal atomic layersin a MXene 2D flake may lead to Mo and Cr being exposed directly to HFduring etching, which leads to their relatively higher removal rateswhile creating their transition metal vacancies in the outer M layers.

The compositions and chemical bonding within the high-entropy MXenes maybe analyzed by conducting X-ray photoelectron spectroscopy (XPS)analysis to evaluate the chemical states as well as the coordination ofthe transition metals and carbon within the high-entropy TiVNbMoC₃T_(x)and TiVCrMoC₃T_(x) MXenes. Specifically, an average distribution of Ti,V, Nb/Cr, Mo, and C may be analyzed by setting the spot size to 400 μmfor the XPS analyses. FIGS. 4A-4F show the XPS high-resolution spectrafor the top surface of as-prepared TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x)MXenes. The C1s high-resolution spectra highlight the existence ofC—Mo/Ti-T_(x), C—Ti/MoT_(x), C—C—CH_(x), C—O, and COO moieties in bothstructures. The Ti2p regions for both TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x)highlights the coordination of Ti as Ti—C and TiO₂ (note that TiO₂ formsdue to surface oxidation of the MXene). The V2p region suggests that Vis coordinated via V²⁺/V⁴⁺ moieties or as V₂O₃, while the Mo3d regionindicates that Mo exists as Mo⁵⁺/Mo⁶⁺, C—Mo-T_(x), and Mo in bothstructures. For TiVNbMoC₃T_(x), the Nb coordination is composed ofseveral species, including Nb⁰, Nb (I, II, or IV) NbO, Nb³⁺—O, Nb⁴⁺—O,and Nb₂O₅, and while in TiVCrMoC₃T_(x), the Cr coordinates as Cr²⁺ andCr⁰. —O and —F groups are also observed, which indicate presence ofsurface moieties on the basal planes of the MXenes (FIG. 11), Table 2and Table 3 include XPS deconvolution data for TiVNbMoC₃T_(x) andTiVCrMoC₃T_(x), respectively.

TABLE 2 TiVNbMoC₃T_(x) Region BE (eV) FWHM (eV) Assigned to Ti 2p 454.8461 1.3 Ti—C 456.6 462.8 3.0 TiO₂ C 1s 282.2 1.0 C—Mo/Ti—T_(x) 282.6 1.0C—Ti/Mo—T_(x) 284.8 1.7 C—C 285.4 1.5 CH_(x) 286.2 2.0 C—O 287.5 2.0 COOO 1s 530 1.5 MoO_(x)/TiO₂/C—Mo—O(I) 530.9 1.1 C—Mo—O(II)x and/or OR531.9 1.2 C—Mo—(OH)_(x) and/or OR 533 1.4 H₂Oads (IV) and/or OR Mo 3d228 231.1 1.1 Mo metal 229.3 232.5 1.1 C—Mo—T_(x) 230.5 233.9 1.3 Mo⁺⁵232 235.1 1.4 Mo⁺⁶ Nb 3d 203.1 205.9 0.7 Nb 203.5 206.3 0.8 Nb 203.8206.6 0.9 Nb (I, II, or IV) 204.1 206.9 0.8 NbO 205.2 208.0 0.9 Nb(³⁺)—O206.7 209.5 0.6 Nb(⁴⁺)—O 207.4 210.2 0.8 Nb₂O₅ V 2p 513.6 521 1.5 V²⁺516.4 523.8 2.0 V⁴⁺ 517.1 524.5 1.5 V₂O₃ O1s 529.6 1.8 TiO₂, MO_(x)531.0 1.4 C—M—O_(x) (I) 532.0 1.5 C—M—OH_(x) (II) 532.9 2.0 Al₂O₃ 534.02.0 H₂O_(ads) (IV) F1s 684.6 2.3 M—F

TABLE 3 TiVCrMoC₃T_(x) Region be (eV) FWHM (eV) Assigned to Ti 2p 454.8461 1.5 Ti—C 456.6 462.8 3.0 TiO₂ C 1s 282.3 1.0 C—Mo/Ti—T_(x) 282.7 1.1C—Ti/Mo—T_(x) 284.8 1.7 C—C 285.5 1.5 CH_(x) 286.3 2.0 C—O 287.6 2.0 COOO 1s 530 1.6 MoO_(x)/TiO₂/C—Mo—O(I) 530.9 1.2 C—Mo—O(II)_(x) and/or OR531.9 1.2 C—Mo—(OH)_(x) and/or OR 533 1.4 H₂O_(ads) (IV) and/or OR Mo3d228 231.1 1.1 Mo metal 229.3 232.5 1.2 C—Mo—T_(x) 230.5 233.9 1.3 Mo⁺⁵232 235.1 1.4 Mo⁺⁶ Cr2p 574.8 584.1 2.0 Cr—C 576.4 585.7 2.8 Cr—T_(x) V2p 513.6 521 1.5 V²⁺ 515.4 522.8 2.0 v⁴⁺ 517.1 524.5 1.5 V₂O₃ O1s 529.61.6 TiO₂, MO_(x) 531.0 1.9 C—M—O_(x) (I) 532.0 2.0 C—M—OH_(x) (II) 532.91.5 Al₂O₃ 534.0 2.0 H₂O_(ads) (IV) F1s 684.6 2.2 M—F

XPS depth profiles with Ar⁺ etching may be performed to analyze thedistribution and evaluate the presence of Ti, V, Nb/Cr, Mo, and C inTiVNbMoC₃T_(x) and TiVCrMoC₃T_(x) (FIGS. 4G, 4H). Ar⁺ etching XPS helpsprovide reliable data on the composition of the constituent elements toovercome possible surface oxidation caused by air exposure. The etchingwith Ar⁺ ions at a rate of 0.05 nm/s enabled removal of surfaceimpurities and the relative magnitude of the elemental deviation wasmore apparent after 20-30 s of Ar⁺ etching (FIGS. 4G-4H), which is inagreement with the EDS results on the multi-layer MXenes (Table 1). TheXPS depth profiling indicates that the distribution of Ti, V, Nb/Cr, Mo,and C was relatively constant through the MXene films, suggesting thatthe MXenes have a relatively uniform distribution of the transitionmetals in the structure. With increasing depth, the concentration ofeach transition metal element approaches the equimolar concentration ofthe high-entropy MXenes as observed in their precursor MAX phases. Thisalso indicates that the topochemical etching process in aqueous HF andthe delamination process did not alter the transition metal ratios.

The composition of the synthesized high-entropy MXenes may be furthercharacterized using scanning transmission electron microscopy (STEM)analysis combined with EDS. Specifically, elemental distribution andnanostructure of TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x) flakes may indicate a4-atomic-layer structure with elements mapped. For example, to probe thestructure of MXenes, samples may be drop-cast from delaminated MXenesolutions on a lacey carbon-coated Cu grid. FIG. 4I shows high-angleannular dark-field (HAADF) STEM image of TiVNbMoC₃T_(x), indicating thateach MXene flake is composed of four transition metal atomic layers. EDSmapping (FIG. 4J and FIG. 12) of each MXene compositions reveals thatTi, V, Nb/Cr, Mo, and C are distributed across the transition metallayers, signifying the near equimolar distribution of the transitionmetals in high-entropy MXenes.

Computational studies based on first principles approaches wereperformed to help understand the synthesizability of high-entropy MAXand MXene phases as well as to quantify the thermodynamic stability ofthe MAX compositions. Specifically, the formation enthalpy (ΔH) of theMAX compositions with reference to the combination of most competitivephases, ΔH_(cp)=ΔH_(MAX phase)−ΔH_(competitive phases), was studied. Theformation enthalpy of different phases was calculated using the totalenergy of those phase structures and the total energies (per atom) ofthe M, A, and X elements in their standard state (bulk phases). The mostcompeting phases were then identified using a linear optimizationprocess. The negative ΔH_(cp) specifies the relative stability of MAXphases with respect to the competitive phases. In general, the morenegative enthalpy values indicate higher possibility for theirexperimental realization. The compositions of the MAX phases along withtheir enthalpies of formation as well as lattice parameters are given inTable 4. The Bader charges of the transition metals for bothhigh-entropy MAX phases are also presented in Table 5. The calculatedelectron concentration of the already synthesized MAX phases withreference to their relative formation energies is shown in FIG. 13.

TABLE 4 Most competing ΔH_(cp) Electron Concentration MAX Phases a (Å) b(Å) c (Å) phases (eV/atom) (electron/Å³) (TiVCrMo)AlC₃ 2.985 2.98523.066 Ti₃AlC₂, V₃AlC₂, −0.011 0.405 Cr₃C₂, Mo₃Al, C (TiVNbMo)AlC₃ 3.0553.054 23.601 Ti₃AlC₂, V₃AlC₂, 0.033 0.367 Nb₃AlC₂, MoC(Ti_(1.33)Vi_(1.33)Nb_(1.33))AlC₃ 3.044 3.050 23.557 Ti₃AlC₂, V₃AlC₂,0.014 0.356 Nb₃AlC₂, C

TABLE 5 Composition Ti V Cr/Nb Mo TiVCrMoAlC₃ 1.307 1.121 0.893 0.759TiVNbMoAlC₃ 1.314 1.126 1.308 0.778

Probable reaction paths for formation of high-entropy MAX phases inTable 4 include:

(TiVCrMo)AlC₃

⅓Ti₃AlC₂+⅓V₃AlC₂+⅓Cr₃C₂+⅓Mo₃Al+C

(TiVNbMo)AlC₃

⅓Ti₃AlC₂+⅓V₃AlC₂+⅓Nb₃AlC₂+MoC

(Ti_(1.33)V_(1.33)Nb_(1.33))AlC₃

⅓Ti₃AlC₂+⅓V₃AlC₂+⅓Nb₃AlC₂+C

Table 5 results show that Ti elements gain more charge in TiVNbMoAlC₃than TiVCrMoAlC₃, while the charge of V and Mo elements are identical inboth compositions. Additionally, more charges are transferred to the Nbelement in TiVNbMoAlC₃ composition in comparison to the Cr element inTiVNbMoAlC₃ because the Nb and Cr elements need three and two electronsto fill their valence shell, respectively.

Referring to FIG. 13, no specific value for ΔG_(cp) can be directlyapplied as a constraint for the thermodynamic stabilities of the MAXcandidates. This is because the formation of many metastable materialsis possible by controlling the temperature, pressure, and synthesismethod. However, a lower value of ΔH indicates a higher probability ofthe MAX phase formation. The calculated ΔH_(cp) values (eV/atom) at 0Kelvin for the MAX phases confirm that MAX phases of Sc₂AlC, Ti₂AlC,Ti₃AlC₂, and Ti₄AlC₃ with the ΔH_(cp) values of 0.10, 0.039, 0.039 and0.038 eV/atom respectively, have already been synthesized. Both aninadequate number of valence electrons occupying bonding states and anabundance of valence electrons occupying antibonding states reduce theprobability of the successful synthesis of the MAX candidates.

Electron concentration for the MAX phases that have already beensynthesized with reference to their relative formation energies may becalculated (FIG. 13). As shown, the synthesizability of MAX candidatesis higher in those candidates with an electron concentration close to0.3 (electrons/atom); however, no MAX phases have been formed with theelectron concentration below 0.2 and above 0.43 (electrons/atom).

In multicomponent systems, a major contributor to their stabilizationarises from configurational entropy i.e. statistically the number ofdiscrete representative positions of the alloy constituents which isdependent on the number of elements in the system under consideration.The entropic contribution for the ternary and quaternary MAX systems canbe calculated using:

${\Delta\; S_{mix}} = {{- R}{\sum\limits_{i = 1}^{k}{x_{i}\mspace{11mu}\ln\mspace{11mu} x_{i}}}}$

where x_(i) is the mole fraction of the i^(th) component in a systemwith k total components. The calculated entropic contribution at 1600°C. for ternary and quaternary systems are −0.1773 eV/f.u. and −0.2238eV/f.u. respectively. Based on configurational entropy, the four-elementMAX phase has more favorable entropy to form as a single-phase comparedto the three-element one (FIG. 14). The entropic stabilization explainsthe preference for four-element single-phase MAX phase as compared tothree-element phases of MAX under similar synthesis conditions. Note,however, that our enthalpy calculations reveal that the three-elementMAX is also synthesizable (Table 4). Since only one synthesistemperature and duration (1600° C.-4 h) were used for the consistency,the single-phase formation of the three-element MAX by further annealingat a desired temperature and duration remains a possibility. A lowercontribution of configurational entropy can lead to the formation of amultiphase system (e.g., undesired phases) in the absence ofpost-annealing treatment.

In certain embodiments, various high-entropy MXenes in addition toTiVNbMoC₃ and TiVCrMoC₃ may be prepared following the methods of thepresent disclosure. For example, TiCrMoTaAlC₃ and TiCrNbTaAlC₃high-entropy MAX phases may be prepared via reactive sintering, andthrough etching and delamination, TiCrMoTaC₃ and TiCrNbTaC₃ high-entropyMXene flakes may be obtained. Specifically, high-entropy MAX phasesTiCrMoTaAlC₃ and TiCrNbTaAlC₃ may be synthesized by mixing an equimolarratio of four transition metals Ti, Cr, Mo or Nb, and Ta with Al and CTi:Cr:Mo or Nb:Ta:Al:C in 1:1:1:1:1.1:2.7 stoichiometric ratio, reactivesintering the powders to obtain sintered blocks of the high-entropy MAXphases, and milling (e.g., for 12 h) the sintered blocks of high-entropyMAX phases to obtain fine powders of the high-entropy MAX phases.Reactive sintering may be performed in a tube furnace with the powdermixtures placed in alumina crucibles and by heating the powder mixturesfrom room temperature to 1600° C. at 3.5° C./min in a tube furnace andholding time of 4 hours under argon atmosphere. Further, high-entropyMAX phases TiCrMoTaAlC₃ and TiCrNbTaAlC₃ may be etched using an aqueoushydrofluoric acid (HF) etching process, such as by adding the MAX phasesinto 48% HF for four days at 55° C. to selectively etch Al atomic layersfrom the high-entropy MAX phases followed by repeated washing to aneutral pH. Further, multilayered MXenes obtained from etching mayfurther be delaminated using tetramethylammonium hydroxide (TMAOH) intosingle-to-few-layered MXene flakes, which may be obtained throughfiltration.

Aspects of the present disclosure relate to synthesis of high-entropyTiVNbMoAlC₃ and TiVCrMoAlC₃ MAX phases and further processing them intohigh-entropy TiVNbMoC₃T_(x) and TiVCrMoC₃T_(x) MXenes with an equimolarproportion of Ti:V:Nb:Mo and Ti:V:Cr:Mo principal transition metals.Specifically, the high-entropy MAX phases formed using pressure-lessreactive sintering may be transformed into single-to-few layer MXenes byutilizing hydrofluoric acid-based selective etching followed bytetramethylammonium hydroxide delamination. As supported by XRD, SEM andSTEM analysis, methods of producing high purity high-entropy MAX phasesand subsequent single-to-few layer high-entropy MXenes according toembodiments of the present disclosure have been proven to be effective.Additionally, the bonding characteristics in high-entropy MXenes usingXPS and the equimolar composition of transition metals have beenidentified utilizing EDS in SEM. EDS elemental mapping in STEM furthershows the equimolar distribution of transition metals in the transitionmetal layers in the delaminated single-to-few-layer MXenes. Thefirst-principles calculations trace the synthesizability of quaternaryhigh-entropy MAX to an entropy driven stabilization and highlight theimportance of high configurational entropy in equimolar multi-elementsin forming pure and stable phases of MPE MAX phases. The presentdisclosure discloses effective methods of synthesizing high-entropy MAXand MXene materials by maximizing the configurational entropy tostabilize equimolar, or near equimolar, mixtures in a fashion analogousto that in other disordered multicomponent systems (e.g., bulk ceramicsand metals). Successful synthesis of this new subgroup of high-entropyMPE MXenes adds a large possible compositional space to the growingfamily of MXenes, which can be explored for applications ranging fromenergy storage, catalysis, and microstructural stability in extremeenvironment.

Synthesis of High-Entropy MAX Phases

All elements Ti (325 mesh), V (325 mesh), Mo (250 mesh), Nb (325 mesh),Cr (325 mesh), Al (325 mesh), C (calcinated coke) (325 mesh), andreagents HF (48 wt % aqueous), Tetramethylammonium hydroxide (TMAOH)(25% w/w aqueous) were obtained from Fisher Scientific and used withoutfurther processing unless specified. For Al and C, additional amount(˜0.1 moles) of Al were added to compensate for any evaporation duringthe MAX synthesis. In general, the Al to transition metal ratio in MAXphases of similar structures (M₄AC₃ here) is similar regardless of thetransition metal type. Less than stoichiometric ratio of C were used.Molar ratios of the elemental powders for TiN/Nb/Mo/Al/C andTiN/Cr/Mo/Al/C were 1:1:1:1:1.1:2.7 respectively, and the blends weremilled in polycarbonate jars on a tumbler mill with zirconia balls at apowder to ball weight ratios of 1:5 for 18 h at 60 rpm. Ball milledpowders were transferred to alumina crucibles and sintered in aconventional tube furnace (Carbolite Gero) fitted with an alumina tubeat 1600° C., held for 4 h. The temperature ramp rate was 3.5° C./min.The furnace was flushed with Ar gas for 10-15 min prior to firing of theMAX powders. A constant Ar flow was maintained throughout the run tillthe samples reached room temperature. Post cooling, the synthesized MAXphases were drilled with a TiN-coated drill bit and sieved with a 40 μmsieve to obtained uniform grains of MAX powder for etching.

Synthesis and Delamination of High-Entropy MXenes

MXenes (both TiVNbMoC₃ and TiVCrMoC₃) were synthesized via top-downsynthesis, by selective etching of their respective MAX phases. In atypical experiment, 2 g of MAX was added slowly (˜60 s) to apolycarbonate jar filled with 20 ml of HF (48 wt %) and held at 55° C.with continuous stirring at 400 RPM for 4 days. The etched MXene waswashed repeatedly 4-5 times (˜250 ml with DI water) in a centrifuge at4200 RPM with each typical run lasting 3-5 min. The pH (>6) neutralizedetched MXene cakes were obtained via vacuum-assisted filtration with a2.5 micron cellulose filter paper. The etching process is identical forboth TiVNbMoAlC₃ and TiVCrMoAlC₃ phases. Filtered MXene cakes weresubsequently delaminated with 5 wt % TMAOH with continuous stirring at500-600 RPM for 4 h at 55° C. The delaminated MXenes were washedrepeatedly for 5 times (˜250 ml with DI water) in a centrifuge at 10000RPM with variable times (5-10 min) to bring the pH to ˜6. Thesupernatant was collected and films were made by vacuum-assistedfiltration. FIG. 9 shows the supernatant, clay, and films of TiVCrMoC₃and TiVNbMoC₃ MXenes.

Microstructural Characterization—XRD

The structural characteristics of the MAX phases and MXenes werecharacterized using a Bruker D8 Discover x-ray diffractometer with a CuK(alpha) radiation wavelength of 1.54184 Å paired with the Vantectwo-dimensional detector (XRD²). The scans were carried out from 5-75deg 2θ (0-90°) using step sizes of 5° 2θ with a time step of 60 s/step.MAX phase and multi-layer MXene powders were placed into cylindricalholes on an aluminum substrate with dimensions 5 mm diameter×1.5 mmdepth. The MAX powders were preferentially ordered using a clean glassslide for pressing on the top of the powder samples. TiVNbMoC₃ andTiVCrMoC₃ MXene single-to-few layer films were cut into 5 mm×10 mmrectangular pieces and one of these film pieces was stacked on anamorphous double-sided carbon tape on a clean glass substrate. Thesample height was aligned using dual-focused laser beams. Spectral datawas analyzed with crystal impact software, Match!

Microstructural Characterization—SEM/EDS

A JEOL JSM-7800F FESEM equipped with an in-lens thermal field emissionelectron gun and a conical objective lens with in-tandem upper and lowerelectron detectors was used to collect morphological and compositionaldata of the samples. All specimens were sputter-coated with gold (DentonDesk V Turbo) to enhance conduction on the surface. Energy DispersionSpectroscopy was performed via an EDAX Octane Super Detector andassociated EDAX TEAM software. The working distance (10 mm) andelevation angle (35°) were fixed along with a scale setting of 58 forthe EDS analyses. the dead time for each run was manually adjusted to27-35. A random spot was selected and was analyzed point-wise (at 10spots) with an excitation voltage of 15-25 kV and a peak current of 8-10Amp. A Magnification of 1000 kX was used for obtaining the compositionof the MXene films.

Microstructural Characterization—XPS and STEM/EDS

X-ray photoelectron spectroscopy (XPS) spectra were collected for eachMXene using the free-standing films, made by vacuum filtration of theirdelaminated solutions, on a Thermo K-alpha XPS system with a spot sizeof 400 μm at an energy resolution of 0.1 eV. Ar⁺ sputtering was carriedout with a beam energy of 4 eV and the cluster size was 1000 atoms. Forthe XPS depth profiles, the atomic percentages were calculated for onlyTi, V, Mo, Cr/Nb, and C. All XPS spectra were analyzed using ThermoAvantage, a software package provided through ThermoScientific. Scanningtransmission electron microscopy (STEM) was performed on an FEI TalosTEM/STEM equipped with an EDS detector (Bruker) operated at 200 kV.Elemental maps were collected with a STEM spot size of 6. All S/TEMspecimen were prepared by dispersing freestanding MXene films, made fromdelaminated MXene solutions, in D.I. H₂O and drop-casting the dispersiononto lacey carbon-coated copper grids.

Microstructural Characterization—First-Principles Calculations

To simulate the chemical disorder of actual high entropy MAX whilemaintaining a tractable size for the computational cell, specialquasi-random structures (SQSs) as implemented in the ATAT softwarepackage were ysed. For the quaternary MAX phase, a 2×2×1 supercell wasused whereas in case of ternary system, a supercell of 3×3×1 from theparent MAX phase was used. The Perdue-Burke-Ernzerhof (PBE)exchange-correlation functional and the projected augmented waveapproach were used through its implementation in the Vienna Ab-InitioSimulation Package (VASP). The MAX phase structures were fully optimizedthrough relaxation of the unit-cell shape, atomic positions, and volumeusing the conjugate gradient method until the maximum residual forceacting on each atom became less than 0.01 eV/A. The electronic energyconvergence criterion used is 10⁻⁶ eV/cell having a plane wave cut-offenergy of 520 eV. The Brillouin zone was integrated using Monkhorst-Packk-point sampling method. A dense k-point grid was employed, defined byn_(atoms)×n_(k-points)≈1000, where n_(atoms) is the number of atoms inthe primitive cell and n_(k-points) being the number of k-pointsrespectively.

It should be noted that many alternative or additional functionalrelationships or physical connections may be present in a practicalsystem. However, the benefits, advantages, solutions to problems, andany elements that may cause any benefit, advantage, or solution to occuror become more pronounced are not to be construed as critical, required,or essential features or elements. The scope is accordingly to belimited by nothing other than the claims, in which reference to anelement in the singular is not intended to mean “one and only one”unless explicitly so stated, but rather “one or more.” Moreover, where aphrase similar to “at least one of A, B, or C” is used in the claims, itis intended that the phrase be interpreted to mean that A alone may bepresent in an embodiment, B alone may be present in an embodiment, Calone may be present in an embodiment, or that any combination of theelements A, B or C may be present in a single embodiment; for example, Aand B, A and C, B and C, or A and B and C.

In the detailed description herein, references to “one embodiment,” “anembodiment,” “an example embodiment,” etc., indicate that the embodimentdescribed may include a particular feature, structure, orcharacteristic, but every embodiment may not necessarily include theparticular feature, structure, or characteristic. Moreover, such phrasesare not necessarily referring to the same embodiment. Further, when aparticular feature, structure, or characteristic is described inconnection with an embodiment, it is submitted that it is within theknowledge of one skilled in the art with the benefit of the presentdisclosure to affect such feature, structure, or characteristic inconnection with other embodiments whether or not explicitly described.After reading the description, it will be apparent to one skilled in therelevant art(s) how to implement the disclosure in alternativeembodiments.

Furthermore, no element, component, or method step in the presentdisclosure is intended to be dedicated to the public regardless ofwhether the element, component, or method step is explicitly recited inthe claims. No claim element herein is to be construed under theprovisions of 35 U.S.C. 112(f), unless the element is expressly recitedusing the phrase “means for.” As used herein, the terms “comprises,”“comprising,” or any other variation thereof, are intended to cover anon-exclusive inclusion, such that a process, method, article, orapparatus that comprises a list of elements does not include only thoseelements but may include other elements not expressly listed or inherentto such process, method, article, or apparatus.

Finally, it should be noted that there are alternative ways ofimplementing the embodiments disclosed herein. Accordingly, the presentembodiments are to be considered as illustrative and not restrictive.Furthermore, the claims are not to be limited to the details givenherein and are entitled to their full scope and equivalents thereof.Various modifications and additions can be made to the exemplaryembodiments discussed without departing from the scope of the presentdisclosure. For example, while the embodiments described above refer toparticular features, the scope of this disclosure also includesembodiments having different combinations of features and embodimentsthat do not include all of the described features. Accordingly, thescope of the present disclosure is intended to embrace all suchalternatives, modifications, and variations as fall within the scope ofthe claims, together with all equivalents thereof.

We claim:
 1. A composition of matter defined by the general formula ofM1M2M3M4X₃, wherein: X is carbon; and M1, M2, M3, and M4 each representa different transition metal selected from the group consisting of Ti,Ta, Sc, Cr, Zr, Hf, Mo, V, and Nb.
 2. The composition of claim 1,wherein M1, M2, M3, M4 each represent a different transition metalselected from the group consisting of Ti, Ta, Cr, Mo, V, and Nb.
 3. Thecomposition of claim 1, wherein the composition is selected from thegroup consisting of TiVNbMoC₃ and TiVCrMoC₃.
 4. The composition of claim1, wherein the composition is a MXene.
 5. The composition of claim 1,wherein the composition is produced by at least: preparing precursor MAXphase powder; etching the MAX phase powder to obtain multi-layered MXenepowder; and delaminating the multi-layered MXene powder to obtainsingle-to-few-layered MXene flakes.
 6. The composition of claim 5,wherein preparing precursor MAX phase powder includes mixing andreactive sintering elemental powders of equimolar ratio of fourtransition metals M¹, M², M³, and M⁴ with Al and C M¹:M²:M³:M⁴:Al:C in1:1:1:1:1.1:2.7 stoichiometric ratio to obtain one or more sintered MAXphase blocks.
 7. The composition of claim 6, wherein preparing precursorMAX phase powder further includes milling the one or more sintered MAXphase blocks to obtain the MAX phase powder.
 8. The composition of claim5, wherein etching the MAX phase powder includes adding the MAX phasepowder into an aqueous hydrofluoric acid to selectively etch away Al toobtain multi-layered MXene powder.
 9. The composition of claim 5,wherein delaminating the multi-layered MXene powder includesdelaminating the multi-layered MXene powder using tetramethylammoniumhydroxide (TMAOH).
 10. The composition of claim 9, wherein delaminatingthe multi-layered MXene powder further includes filtering MXene fromTMAOH to obtain the single-to-few-layered MXene flakes.
 11. A method ofproducing a composition of matter defined by the general formula ofM1M2M3M4X₃, the method comprising: preparing precursor MAX phase powder;etching the MAX phase powder to obtain multi-layered MXene powder; anddelaminating the multi-layered MXene powder to obtainsingle-to-few-layered MXene flakes having the general formula ofM1M2M3M4X₃; wherein: X is carbon; and M1, M2, M3, and M4 each representa different transition metal selected from the group consisting of Ti,Ta, Sc, Cr, Zr, Hf, Mo, V, and Nb.
 12. The method of claim 11, whereinM1, M2, M3, M4 each represent a different transition metal selected fromthe group consisting of Ti, Ta, Cr, Mo, V, and Nb.
 13. The method ofclaim 11, wherein the composition is selected from the group consistingof TiVNbMoC₃ and TiVCrMoC₃.
 14. The method of claim 11, wherein thecomposition is a MXene.
 15. The method of claim 11, wherein preparingprecursor MAX phase powder includes mixing and reactive sinteringelemental powders of equimolar ratio of four transition metals M¹, M²,M³, and M⁴ with Al and C M¹:M²:M³:M⁴:Al:C in 1:1:1:1:1.1:2.7stoichiometric ratio to obtain one or more sintered MAX phase blocks.16. The method of claim 15, wherein preparing precursor MAX phase powderfurther includes milling the one or more sintered MAX phase blocks toobtain the MAX phase powder.
 17. The method of claim 11, wherein etchingthe MAX phase powder includes adding the MAX phase powder into anaqueous hydrofluoric acid to selectively etch away Al to obtainmulti-layered MXene powder.
 18. The method of claim 11, whereindelaminating the multi-layered MXene powder includes delaminating themulti-layered MXene powder using tetramethylammonium hydroxide (TMAOH).19. The method of claim 18, wherein delaminating the multi-layered MXenepowder further includes filtering MXene from TMAOH to obtain thesingle-to-few-layered MXene flakes.
 20. A composition of matter definedby the general formula of M1M2M3M4AX₃, wherein: X is carbon; A isaluminum; and M1, M2, M3, and M4 each represent a different transitionmetal selected from the group consisting of Ti, Ta, Sc, Cr, Zr, Mo, V,and Nb.